Strange Sorting

AtCoder

IDagc014_f

Time2000ms

Memory256MB

Difficulty—

Takahashi loves sorting. He has a permutation $(p_1,p_2,...,p_N)$ of the integers from $1$ through $N$. Now, he will repeat the following operation until the permutation becomes $(1,2,...,N)$: * First, we will define _high_ and _low_ elements in the permutation, as follows. The $i$\-th element in the permutation is high if the maximum element between the $1$\-st and $i$\-th elements, inclusive, is the $i$\-th element itself, and otherwise the $i$\-th element is low. * Then, let $a_1,a_2,...,a_k$ be the values of the high elements, and $b_1,b_2,...,b_{N-k}$ be the values of the low elements in the current permutation, **in the order they appear in it**. * Lastly, rearrange the permutation into $(b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k)$. How many operations are necessary until the permutation is sorted? ## Constraints * $1 ≤ N ≤ 2×10^5$ * $(p_1,p_2,...,p_N)$ is a permutation of the integers from $1$ through $N$. ## Input Input is given from Standard Input in the following format: $N$ $p_1$ $p_2$ ... $p_N$ [samples]

Samples

Input #1

5
3 5 1 2 4

Output #1

3

The initial permutation is $(3,5,1,2,4)$, and each operation changes it as follows:

*   In the first operation, the $1$\-st and $2$\-nd elements are high, and the $3$\-rd, $4$\-th and $5$\-th are low. The permutation becomes: $(1,2,4,3,5)$.
*   In the second operation, the $1$\-st, $2$\-nd, $3$\-rd and $5$\-th elements are high, and the $4$\-th is low. The permutation becomes: $(3,1,2,4,5)$.
*   In the third operation, the $1$\-st, $4$\-th and $5$\-th elements are high, and the $2$\-nd and $3$\-rd and $5$\-th are low. The permutation becomes: $(1,2,3,4,5)$.

Input #2

5
5 4 3 2 1

Output #2

Input #3

10
2 10 5 7 3 6 4 9 8 1

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Strange Sorting",
    "description": {
      "content": "Takahashi loves sorting. He has a permutation $(p_1,p_2,...,p_N)$ of the integers from $1$ through $N$. Now, he will repeat the following operation until the permutation becomes $(1,2,...,N)$: *   Fi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc014_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi loves sorting.\nHe has a permutation $(p_1,p_2,...,p_N)$ of the integers from $1$ through $N$. Now, he will repeat the following operation until the permutation becomes $(1,2,...,N)$:\n\n*   Fi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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